Доказать, что [tex] \sqrt{11...1 - 22...2}=33...3 [/tex]. 11....1-100 раз, 22...2-50 раз и 33...3-50 раз. Created by Vampire100. algebra-ru

tex]. 11....1-100 раз, 22...2-50 раз и 33...3-50 раз...

Vampire100 @Vampire100

July 2022 1 18 Report

Доказать, что [tex] \sqrt{11...1 - 22...2}=33...3
[/tex]. 11....1-100 раз, 22...2-50 раз и 33...3-50 раз

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arsenlevadniy

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$\sqrt{ \underbrace{11...1}\limits_{100} - \underbrace{22...2}\limits_{50}} = \underbrace{33...3}\limits_{50}, \\ \sqrt{\underbrace{11...1}\limits_{50}\cdot(1\underbrace{00...0}\limits_{49}1 - 2)} = \sqrt{\underbrace{11...1}\limits_{50}\cdot\underbrace{99...9}\limits_{50}} = \sqrt{\underbrace{11...1}\limits_{50}\cdot\underbrace{11...1}\limits_{50}\cdot9} = \\ = \sqrt{(\underbrace{11...1}\limits_{50})^2\cdot9} = \underbrace{11...1}\limits_{50}\cdot3 = \underbrace{33...3}\limits_{50}$

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